Answer:
x = 25, y = 9
Step-by-step explanation:
Since the triangles are congruent then corresponding angles and sides are congruent, thus
∠ O = ∠ P , substitute values
6y - 14 = 40 ( add 14 to both sides )
6y = 54 ( divide both sides by 6 )
y = 9
and
NG = IT , that is
x - 2y = 7 ( substitute y = 9 into the equation )
x - 2(9) = 7
x - 18 = 7 ( add 18 to both sides )
x = 25
Answer:
12, 15, 18
Step-by-step explanation:
4x+5x+6x=45
15x=45
x=3
4x=12, 5x=15, 6x= 18
Answer:
Segment BF = 16
Step-by-step explanation:
The given theorem states that a line parallel to one side of a triangle divides the other two sides proportionately
The given theorem is the Triangle Proportionality Theorem
According to the theorem, given that segment DE is parallel to segment BC, we have;
Therefore;
Which gives;
Similarly, given that EF is parallel to AB, we get;
Therefore;
Which gives;
Therefore, the statement that can be proved using the given theorem is segment BF = 16.
For this case, what we must do is solve the following system of equations:
tan (50) = h / x
tan (40) = h / (x + 50)
Solving the system we have:
(x + 50) * tan (40) = h
(x) * tan (50) = h
Matching:
(x + 50) * tan (40) = (x) * tan (50)
Rewriting:
x (tan (50) - tan (40)) = 50 * tan (40)
x = 50 * tan (40) / (tan (50) - tan (40))
x = 118.9692621
Substituting:
h = (x) * tan (50)
h = (118.9692621) * tan (50)
h = 141.7820455
Answer:
The height of the building is:
h = 141.7820455 ft
